U.S. patent application number 11/551850 was filed with the patent office on 2007-09-27 for characterization of receiver demodulation for correcting off-axis mr imaging degradation.
Invention is credited to Walter F. Block, Yogesh Arvind Jashnani, Youngkyoo Jung.
Application Number | 20070222446 11/551850 |
Document ID | / |
Family ID | 37833579 |
Filed Date | 2007-09-27 |
United States Patent
Application |
20070222446 |
Kind Code |
A1 |
Jung; Youngkyoo ; et
al. |
September 27, 2007 |
CHARACTERIZATION OF RECEIVER DEMODULATION FOR CORRECTING OFF-AXIS
MR IMAGING DEGRADATION
Abstract
A calibration procedure is performed prior to an off-axis MR
scan to measure the MRI system timing errors in applying a
frequency modulation waveform to the system receiver. Phase errors
which otherwise occur when performing non-Cartesian scans are
either prospectively reduced by offsetting the timing error or
retrospectively offset by applying phase corrections to the
acquired image data.
Inventors: |
Jung; Youngkyoo; (Madison,
WI) ; Jashnani; Yogesh Arvind; (Richmond, VA)
; Block; Walter F.; (Madison, WI) |
Correspondence
Address: |
QUARLES & BRADY LLP
411 E. WISCONSIN AVENUE, SUITE 2040
MILWAUKEE
WI
53202-4497
US
|
Family ID: |
37833579 |
Appl. No.: |
11/551850 |
Filed: |
October 23, 2006 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
11289960 |
Nov 30, 2005 |
7132826 |
|
|
11551850 |
Oct 23, 2006 |
|
|
|
Current U.S.
Class: |
324/307 |
Current CPC
Class: |
G01R 33/4833 20130101;
G01R 33/56581 20130101; G01R 33/56518 20130101; G01R 33/56563
20130101; G01R 33/58 20130101; G01R 33/565 20130101 |
Class at
Publication: |
324/307 |
International
Class: |
G01V 3/00 20060101
G01V003/00 |
Goverment Interests
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH
[0002] This invention was made with government support under Grant
No. NIH EB002075. The United States Government has certain rights
in this invention.
Claims
1. A method for calibrating a magnetic resonance imaging (MRI)
system prior to the acquisition of an image that is offset from the
system isocenter, the steps comprising: a) performing a pulse
sequence with the MRI system while acquiring a first NMR free
induction decay (FID) signal; b) producing a first calibration
phase data set .phi..sub.1(t) by calculating a phase at each of a
plurality of points during the first FID signal; c) performing the
pulse sequence with the MRI system while applying a frequency
demodulation waveform .DELTA.f(t) to the MRI system receiver to
acquire a second NMR FID signal; d) producing a second calibration
phase data set .phi..sub.2(t) by calculating a phase at each of a
plurality of points during the second FID signal; e) calculating
ideal phase data .phi..sub.NOMINAL(t) from the frequency modulation
waveform .DELTA.f(t); f) calculating phase error
E.sub..phi..DELTA.f(t) according to the following equation:
E.sub..phi..DELTA.f(t)=.phi..sub.2(t) -[.phi..sub.1(t)
-.phi..sub.NOMINAL(t)]; and g) calculating a timing error
.tau..sub.D representative of a delay between the applied frequency
demodulation waveform .DELTA.f(t) and the NMR signal using the
phase error E.sub..phi..DELTA.f(t) calculated in step f).
2. The method as recited in claim 1 in which step f) further
includes calculating .phi..sub.NOMINAL(t) according to the equation
.PHI. NOMINAL = 2 .times. .pi. .times. .intg. 0 t .times. .DELTA.
.times. .times. f .function. ( t ) .times. .times. d t .
##EQU8##
3. The method as recited in claim 1 in which step g) includes
calculating from the phase error E.sub..phi..DELTA.f(t) a maximum
phase error E.sub..phi.PLATEAU.
4. The method as recited in claim 3 in which step g) further
includes calculating the timing error .tau..sub.D according to the
following expression:
.tau..sub.D=E.sub..phi.PLATEAU/2.pi..DELTA.f.sub.P where:
.DELTA.f.sub.P=the amplitude of the frequency demodulation waveform
.DELTA.f(t).
5. The method as recited in claim 1 which further includes using
the timing error to prospectively correct image data subsequently
acquired with the MRI system.
6. The method as recited in claim 1 which further includes
retrospectively correcting image data subsequently acquired with
the MRI system using the timing error.
7. The method as recited in claim 6 in which the image data is
corrected by applying a phase shift thereto.
8. The method as recited in claim 7 wherein the phase shift takes
into account the actual gradient waveforms.
9. The method as recited in claim 1 which further includes
prospectively correcting for the timing error using a real-time
phase demodulation.
Description
CROSS REFERENCES TO RELATED APPLICATIONS
[0001] This application is a continuation-in-part application of
and claims the benefit of U.S. patent application Ser. No.
11/289,960, filed Nov. 20, 2005 and titled "Characterization of
Receiver Demodulation for Correcting Off-Axis Imaging
Degradation".
BACKGROUND OF THE INVENTION
[0003] The field of the invention is nuclear magnetic resonance
imaging (MRI) methods and systems. More particularly, the invention
relates to characterization of various timing delays in an off-axis
MRI system.
[0004] When a substance such as human tissue is subjected to a
uniform magnetic field (polarizing field BO), the individual
magnetic moments, commonly called spins, in the tissue attempt to
align with this polarizing field, but precess about it in random
order at their characteristic Larmor frequency. If the substance,
or tissue, is subjected to a magnetic field (excitation field
B.sub.1) which is in the x-y plane and which is near the Larmor
frequency, the net aligned moment, Mz, may be rotated, or "tipped",
into the x-y plane to produce a net transverse magnetic moment Mt.
A signal is emitted by the excited spins after the excitation
signal B.sub.1 is terminated, and this signal may be received and
processed to form an image.
[0005] When utilizing these signals to produce images, magnetic
field gradients (G.sub.x, G.sub.y and (G.sub.z) are employed.
Typically, the region to be imaged is scanned by a sequence of
measurement cycles in which these gradients vary according to the
particular localization method being used. The resulting set of
received NMR signals are digitized and processed to reconstruct the
image using one of many well known reconstruction techniques.
[0006] A number of imaging techniques use the spin warp method,
sometimes referred to as the Fourier transform (FT) method, in
which one or two magnetic field gradients phase encode spatial
information in the direction of the gradient. In a two-dimensional
implementation (2DFT), for example, spatial information is encoded
in one direction by applying a phase encoding gradient along one
gradient direction, and then a gradient echo or a spin-echo signal
is acquired in the presence of a readout magnetic gradient in a
direction orthogonal to the phase encoding gradient. In a typical
2DFT scan, the magnitude of the phase encoding gradient pulse is
incremented in the sequence of views that are acquired and Fourier
space, or "k-space" is sampled in a Cartesian grid. Most scans
currently performed on MRI systems employ such 2DFT or 3DFT
techniques.
[0007] There are a number of MR imaging techniques which do not use
the Fourier transform method of sampling k-space in a Cartesian
grid. These include spiral techniques such as that described in
U.S. Pat. Nos. 6,215,305 and 6,404,194; projection reconstruction,
or radial, techniques such as that described in U.S. Pat. No.
6,794,867; and shell k-space sampling techniques such as that
described in U.S. Pat. No. 5,532,595. A common element of these
non-Cartesian sampling techniques is that the imaging gradient
field changes strength and is time-varying during the read-out of
the NMR signal.
[0008] Non-Cartesian imaging techniques have several benefits in
accelerating magnetic resonance imaging. However, these techniques
are more sensitive to system instabilities caused by eddy currents
and hardware delays that vary from MRI system to system. While
forms of these faster imaging methods are available on clinical
platforms, they are generally considered to create artifacts not
seen in conventional Cartesian imaging. However, they are used
heavily because their speed allows them to capture physiological
processes not possible with Cartesian imaging.
[0009] One clinical application that is particularly problematic
for non-Cartesian imaging techniques is off axis imaging. Imaging
off axis or off isocenter in MRI is often necessary because the
anatomy of interest cannot be placed at the center of the magnet.
Common situations include the knee, shoulder, and heart. Off axis
imaging using a Cartesian pulse sequence is easily managed by
introducing a constant frequency shift, or equivalent linear phase
shift in the received NMR signal which effectively shifts the
center of the reconstructed image away from the system isocenter.
This is commonly done by modifying the phase of the reference
signal used to demodulate the received NMR signals. In Cartesian
imaging, this is done by offsetting the frequency of the reference
signal for imaging offsets along the readout gradient direction or
creating a linear shifting of the phase of the acquired k-space
data in the phase-encoding gradient direction. In the readout
direction, the required phase shifts are linearly proportional to
the image offset along the readout gradient axis and the strength
of the readout gradient. When non-Cartesian pulse sequences are
used, however, this strategy becomes much more difficult because
the time-varying gradients can be considered to be changing the
direction and the strength of the readout gradient. The phase shift
is no longer simply linear and must be changed in real time as the
changing gradient waveforms are played out during the NMR signal
acquisition.
SUMMARY OF THE INVENTION
[0010] The present invention stems from the recognition that many
of the image artifacts produced by non-Cartesian imaging techniques
when performing off axis imaging are due to phase errors introduced
by the real-time demodulation hardware within the MRI system. The
phase errors can be attributed to a timing delay E.sub.t between
the real-time demodulation hardware and the generation of the
gradient fields, or to a timing delay .tau..sub.D between the
real-time demodulation hardware and the data acquisition hardware.
These timing delays may vary from scanner to scanner. In the
present invention, a calibration procedure is performed during a
pre-scan to measure one or more timing delays which cause the phase
errors. Correction can be made prospectively during the subsequent
scan by offsetting the timing error during data acquisition, or it
can be made retrospectively by phase correcting the acquired
data.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] FIG. 1 is a block diagram of an MRI system which employs the
present invention;
[0012] FIG. 2 is a block diagram of the RF system which forms part
of the MRI system of FIG. 1;
[0013] FIG. 3 is a flow chart of one embodiment of a calibration
procedure which is part of a prescan process employed by the MRI
system of FIG. 1;
[0014] FIG. 4 is a graphic representation of a pulse sequence
performed by the MRI system while practicing the calibration method
of FIG. 3;
[0015] FIG. 5 is a graphic representation of waveforms produced
while practicing the calibration method of FIG. 3;
[0016] FIG. 6 is a flow chart of another embodiment of a
calibration procedure which is part of a prescan process employed
by the MRI system of FIG. 1; and
[0017] FIG. 7 is a graphic representation of a pulse sequence
performed by the MRI system and waveforms produced while practicing
the calibration procedure of FIG. 6.
DETAILED DESCRIPTION
[0018] Referring particularly to FIG. 1, the preferred embodiment
of the invention is employed in an MRI system. The MRI system
includes a workstation 10 having a display 12 and a keyboard 14.
The workstation 10 includes a processor 16 which is a commercially
available programmable machine running a commercially available
operating system. The workstation 10 provides the operator
interface which enables scan prescriptions to be entered into the
MRI system.
[0019] The workstation 10 is coupled to four servers: a pulse
sequence server 18; a data acquisition server 20; a data processing
server 22, and a data store server 23. In the preferred embodiment
the data store server 23 is performed by the workstation processor
16 and associated disc drive interface circuitry. The remaining
three servers 18, 20 and 22 are performed by separate processors
mounted in a single enclosure and interconnected using a 64-bit
backplane bus. The pulse sequence server 18 employs a commercially
available microprocessor and a commercially available quad
communication controller. The data acquisition server 20 and data
processing server 22 both employ the same commercially available
microprocessor and the data processing server 22 further includes
one or more array processors based on commercially available
parallel vector processors.
[0020] The workstation 10 and each processor for the servers 18, 20
and 22 are connected to a serial communications network. This
serial network conveys data that is downloaded to the servers 18,
20 and 22 from the workstation 10 and it conveys tag data that is
communicated between the servers and between the workstation and
the servers. In addition, a high speed data link is provided
between the data processing server 22 and the workstation 10 in
order to convey image data to the data store server 23.
[0021] The pulse sequence server 18 functions in response to
program elements downloaded from the workstation 10 to operate a
gradient system 24 and an RF system 26. Gradient waveforms
necessary to perform the prescribed scan are produced and applied
to the gradient system 24 which excites gradient coils in an
assembly 28 to produce the magnetic field gradients G.sub.x,
G.sub.y and G.sub.z, used for position encoding NMR signals. The
gradient coil assembly 28 forms part of a magnet assembly 30 which
includes a polarizing magnet 32 and a whole-body RF coil 34.
[0022] RF excitation waveforms are applied to the RF coil 34 by the
RF system 26 to perform the prescribed magnetic resonance pulse
sequence. Responsive NMR signals detected by the RF coil 34 are
received by the RF system 26, amplified, demodulated, filtered and
digitized under direction of commands produced by the pulse
sequence server 18. The RF system 26 includes an RF transmitter for
producing a wide variety of RF pulses used in MR pulse sequences.
The RF transmitter is responsive to the scan prescription and
direction from the pulse sequence server 18 to produce RF pulses of
the desired frequency, phase and pulse amplitude waveform. The
generated RF pulses may be applied to the whole body RF coil 34 or
to one or more local coils or coil arrays.
[0023] The RF system 26 also includes one or more RF receiver
channels. Typically, the MRI system will have from 1 to 32 receive
channels which may be connected to a corresponding plurality of
local coils or to a corresponding plurality of coil elements in a
coil array. Each RF receive channel includes an RF amplifier that
amplifies the NMR signal received by the coil to which it is
connected and a quadrature detector which detects and digitizes the
I and Q quadrature components of the received NMR signal. The
magnitude of the received NMR signal may thus be determined at any
sampled point by the square root of the sum of the squares of the I
and Q components: M= {square root over (I.sup.2+Q.sup.2)}, and the
phase of the received NMR signal may also be determined:
.phi.=tan.sup.-1 Q/I.
[0024] The pulse sequence server 18 also optionally receives
patient data from a physiological acquisition controller 36. The
controller 36 receives signals from a number of different sensors
connected to the patient, such as ECG signals from electrodes or
respiratory signals from a bellows. Such signals are typically used
by the pulse sequence server 18 to synchronize, or "gate", the
performance of the scan with the subject's respiration or heart
beat.
[0025] The pulse sequence server 18 also connects to a scan room
interface circuit 38 which receives signals from various sensors
associated with the condition of the patient and the magnet system.
It is also through the scan room interface circuit 38 that a
patient positioning system 40 receives commands to move the patient
to desired positions during the scan.
[0026] It should be apparent that the pulse sequence server 18
performs real-time control of MRI system elements during a scan. As
a result, it is necessary that its hardware elements be operated
with program instructions that are executed in a timely manner by
run-time programs. The description components for a scan
prescription are downloaded from the workstation 10 in the form of
objects. The pulse sequence server 18 contains programs which
receive these objects and converts them to objects that are
employed by the run-time programs.
[0027] The digitized NMR signal samples produced by the RF system
26 are received by the data acquisition server 20. The data
acquisition server 20 operates in response to description
components downloaded from the workstation 10 to receive the
real-time NMR data and provide buffer storage such that no data is
lost by data overrun. In some scans the data acquisition server 20
does little more than pass the acquired NMR data to the data
processor server 22. However, in scans which require information
derived from acquired NMR data to control the further performance
of the scan, the data acquisition server 20 is programmed to
produce such information and convey it to the pulse sequence server
18. For example, during prescans NMR data is acquired and used to
calibrate the pulse sequence performed by the pulse sequence server
18. Also, navigator signals may be acquired during a scan and used
to adjust RF or gradient system operating parameters or to control
the view order in which k-space is sampled. And, the data
acquisition server 20 may be employed to process NMR signals used
to detect the arrival of contrast agent in an MRA scan. In all
these examples the data acquisition server 20 acquires NMR data and
processes it in real-time to produce information which is used to
control the scan.
[0028] The data processing server 22 receives NMR data from the
data acquisition server 20 and processes it in accordance with
description components downloaded from the workstation 10. Such
processing may include, for example: Fourier transformation of raw
k-space NMR data to produce two or three-dimensional images; the
application of filters to a reconstructed image; the performance of
a backprojection image reconstruction of acquired NMR data; the
calculation of functional MR images; the calculation of motion or
flow images, etc.
[0029] Images reconstructed by the data processing server 22 are
conveyed back to the workstation 10 where they are stored.
Real-time images, if available, are stored in a data base memory
cache (not shown) from which they may be output to operator display
12 or a display 42 which is located near the magnet assembly 30 for
use by attending physicians. Batch mode images or selected real
time images are stored in a host database on disc storage 44. When
such images have been reconstructed and transferred to storage, the
data processing server 22 notifies the data store server 23 on the
workstation 10. The workstation 10 may be used by an operator to
archive the images, produce films, or send the images via a network
to other facilities.
[0030] As shown in FIG. 1, the RF system 26 may be connected to the
whole body rf coil 34, or as shown in FIG. 2, a transmitter section
of the RF system 26 may connect to one rf coil 152A and its
receiver section may connect to a separate rf receive coil 152B.
Often, the transmitter section is connected to the whole body rf
coil 34 and each receiver section is connected to a separate local
coil 152B.
[0031] Referring particularly to FIG. 2, the RF system 26 includes
a transmitter that produces a prescribed rf excitation field. The
base, or carrier, frequency of this RF excitation field is produced
under control of a frequency synthesizer 200 which receives a set
of digital signals from the pulse sequence server 18. These digital
signals indicate the frequency (f) and phase (.theta.) of the RF
carrier signal produced at an output 201. The RF carrier is applied
to a modulator and up converter 202 where its amplitude is
modulated in response to a signal R(t) also received from the pulse
sequence server 18. The signal R(t) defines the envelope of the RF
excitation pulse to be produced and is produced by sequentially
reading out a series of stored digital values. These stored digital
values may be changed to enable a wide variety of desired RF pulse
envelopes to be produced.
[0032] The magnitude of the RF excitation pulse produced at output
205 is attenuated by an exciter attenuator circuit 206 which
receives a digital command from the pulse sequence server 18. The
attenuated RF excitation pulses are applied to the power amplifier
151 that drives the RF coil 152A. For a more detailed description
of this transmitter section reference is made to U.S. Pat. No.
4,952,877 which is incorporated herein by reference.
[0033] Referring still to FIG. 2 the signal produced by the subject
is picked up by the receiver coil 152B and applied through a
preamplifier 153 to the input of a receiver attenuator 207. The
receiver attenuator 207 further amplifies the signal by an amount
determined by a digital attenuation signal received from the pulse
sequence server 18. The received signal is at or around the Larmor
frequency, and this high frequency signal is down converted in a
two step process by a down converter 208 which first mixes the NMR
signal with the carrier signal on line 201 and then mixes the
resulting difference signal with a reference signal on line 204.
The down converted NMR signal is applied to the input of an
analog-to-digital (A/D) converter 209 which samples and digitizes
the analog signal and applies it to a digital detector and signal
processor 210 which produces 16-bit in-phase (I) values and 16-bit
quadrature (Q) values corresponding to the received signal. The
resulting stream of digitized I and Q values of the received signal
are output to the data acquisition server 20. The reference signal
as well as the sampling signal applied to the A/D converter 209 are
produced by a reference frequency generator 203. For a more
detailed description of the receiver, reference is made to U.S.
Pat. No. 4,992,736 which is incorporated herein by reference.
[0034] To produce an image which is offset from the MRI system
isocenter the frequency of the reference signal on line 201 is
shifted by an amount .DELTA.f which is determined by the magnitude
of imaging gradients being applied as the NMR signal is acquired.
This is described in U.S. Pat. No. 5,689,186 entitled "Method For
Producing An Off-Center Image Using An EPI Pulse Sequence":
.DELTA.f=-.gamma.(G.sub.xd.sub.x+G.sub.yd.sub.y) (1) where
.gamma.=gyromagnetic ratio for spins;
[0035] G.sub.x=gradient along x-axis;
[0036] d.sub.x=offset of FOV along x-axis;
[0037] G.sub.y=gradient along y-axis; and
[0038] d.sub.y=offset of FOV along y-axis.
[0039] In non-Cartesian acquisitions one or more of the gradients
changes in amplitude during the NMR signal acquisition and as a
result, this frequency shift .DELTA.f changes as a function of time
.DELTA.f(t) as the gradient wavefoims G.sub.x(t) and G.sub.y(t) are
played out by the pulse sequence server 18. This frequency shift
function is applied to the frequency synthesizer 200 by the pulse
sequence server 18 and the frequency shift .DELTA.f(t) is applied
to the down converter 208 which demodulates the acquired NMR
signal.
[0040] Timing errors between the A/D converter and the playout of
the gradient fields G.sub.x(t) and G.sub.y(t) in the bore of the
magnet are important in both off-axis and on-aspect imaging.
Methods exist to measure these differences accurately. One aspect
of this invention is the discovery that even small timing
discrepancies exist between the application of this frequency shift
.DELTA.f(t) to the down converter 208 and the initiation of
sampling on the A/D converter 212. This error will produce
substantial phase errors (E.sub..DELTA.f(t)) in the acquired NMR
data. The present invention is a method for measuring this timing
error which can be done as part of a prescan procedure for each
patient and a method of compensating, or correcting the
subsequently acquired NMR data.
[0041] When an off-axis image is to be acquired, the scan
prescription will include one or more scan parameters that indicate
the offset distance from the system isocenter along one or more
gradient axes G.sub.x, G.sub.y, G.sub.z. A prescan process
illustrated in FIG. 3 is used to calculate a timing error between
the frequency synthesizer 201 and the A/D converter 212. The first
step in the calibration process as indicated by process block 300
is to acquire calibration data .theta..sub.1(t) from a slice that
is located a distance D from the system isocenter along one
gradient axis. The pulse sequence used is illustrated in FIG. 4 and
includes a slice-select gradient waveform 302 applied with a
selective 90.degree. RF excitation pulse 304 to excite spins in the
slice. A bipolar gradient waveform 306 directed along the gradient
axis is applied a short time thereafter, and an NMR signal is
acquired simultaneously as indicated by acquisition window 308. The
phase of the acquired k-space samples are calculated as described
above and stored. The pulse sequence can be repeated a number of
times (e.g., 20) and averaged to increase the SNR of the
measurement. The phase of the measurement serves as the calibration
data set .theta..sub.1(t).
[0042] The next step indicated at process block 310 in FIG. 3 is to
acquire a second set of calibration phase data .theta..sub.2(t).
This employs the same pulse sequence shown in FIG. 4, but this time
a frequency modulation .DELTA.f(t) is applied to the receiver as
described above to offset the slice a distance D along the gradient
axis being calibrated. As shown in FIG. 4, the frequency modulation
.DELTA.f(t) is a bipolar waveform 312 that is shaped like the
gradient waveform G(t) and is intended to track the phase produces
by the gradient G(t) at the offset location D as indicated above in
Equation (1). The pulse sequence is repeated and the phase of the
k-space samples acquired during the window 308 are averaged to
produce calibration data set .theta..sub.2(t).
[0043] The next step as indicated by process block 314 is to
calculate the phase of the acquired NMR signal samples based on the
prescribed gradient waveform G(t). This is done as follows: .theta.
IDEAL .function. ( t ) = .intg. t 1 t 2 .times. .gamma. .times.
.times. DG .function. ( t ) .times. .times. d t ( 2 ) ##EQU1##
where .gamma. is the gyromagnetic ratio, D is the distance from the
isocenter and the interval t.sub.1 to t.sub.2 is the time period
during which the gradient waveform is played out. It is also the
time that the NMR signal is acquired as shown in FIG. 4. This is
the theoretical, or ideal, phase that the acquired NMR signal from
the test slice should have if there were no phase errors of any
kind in the MRI system.
[0044] As indicated at process block 316, a phase error
E.sub..DELTA.f(t) is now calculated from the phase values
.theta..sub.1(t), .theta..sub.2(t) and .theta..sub.IDEAL(t). The
phase values .theta..sub.1(t) are measurements which include the
ideal phase shifts .theta..sub.IDEAL(t) plus phase errors due to
B.sub.0 field inhomogeneities E.sub.B and phase errors E.sub.GRAD
due to such factors as gradient-induced eddy currents and
concomitant gradients:
.theta..sub.1(t)=.theta.IDEAL(t)+E.sub.B+E.sub.GRAD. (3) The phase
values .theta..sub.2(t) are measurements which include three phase
error components: E.sub.B; E.sub.GRAD; and a phase error component
E.sub..DELTA.f(t) caused by an inaccurate application of the
frequency modulation waveform .DELTA.f(t) to the receiver:
.theta..sub.2(t)=E.sub.B+E.sub.GRAD+E.sub..DELTA.f(t). (4) The
phase error E.sub..DELTA.f(t) is calculated by combining equations
3 and 4 as follows:
E.sub..DELTA.f(t)=.theta..sub.2(t)-[.theta..sub.1(t)-.theta..su-
b.IDEAL(t)]. (5)
[0045] The phase error E.sub..DELTA.f(t) is shown in FIG. 5, for
example, where there is a timing error E.sub.t between the
application of the gradient waveform 306 to the subject being
imaged and the application of the .DELTA.f(t) frequency modulation
waveform 312 to the receiver. However, it has been discovered that
in most measurements an additional phase error is introduced due to
miscalibrations of the gradient amplifier strength that causes a
slightly inaccurate slice location in the calibration pulse
sequence of FIG. 4. The miscalibration causes slightly more or
slightly less phase accumulation over the test slice during the
bipolar gradient waveform. The phase error looks similar to the
k-space trajectory of the bipolar gradient waveform and has the
appearance of a half cycle of a sine wave. While these
miscalibrations are insignificant in clinical imaging, they add a
bias that alters the phase error signal so that it usually looks
like the waveform 318. To eliminate this additional phase error and
calculate the maximum phase error E.sub..theta.max due solely to
mistiming E.sub.t, the average value in two regions A and B which
are symmetrically disposed to either side of an axis 320 are
employed. As indicated at process block 322, maximum phase error
E.sub..theta.max is then calculated according to the following
equation: E .theta. max = Average .function. ( A ) - Average
.function. ( B ) 2 . ( 6 ) ##EQU2## The maximum phase error
E.sub..theta.max is related to the timing error E.sub.t by the
following expression:
E.sub..theta.max=2.pi..gamma.G.sub.maxDE.sub.t. (7) As indicated at
process block 324, equation (7) can then be solved for the timing
error E.sub.t as follows:
E.sub.t=E.sub..theta.max/2.pi..gamma.DG.sub.max. (8) The timing
error between applied gradient fields and the applied .DELTA.f(t)
frequency modulation waveform may thus be calculated with a high
degree of accuracy.
[0046] Referring again to FIG. 3, the timing error E.sub.t should
be independent of the gradient axes used to produce the phase
change in the slice offset distance D, however, in one embodiment
the process is repeated for each separate imaging gradient. When
the timing error has been measured for each gradient axes as
determined at decision block 326, the timing errors are stored as
indicated at process block 328 and the calibration process is
exited.
[0047] Another aspect of the invention is the realization that
instead of determining a timing delay E.sub.t (for each gradient
axis if desired) while applying a gradient and a Af waveform to the
receiver such as described above, it is also possible to perform a
calibration that calculates a timing delay .tau..sub.D without
using gradients and to then use this delay to correct acquired k
space samples. This further simplifies a prescan procedure for each
patient. Such an embodiment of a prescan process for an off-axis
image acquisition is illustrated in FIG. 6 and is used to calculate
a timing error .tau..sub.D.
[0048] The first step in the calibration process as indicated by
process block 600 is to acquire a first set of calibration phase
data .PHI..sub.1(t) from a slice that is located a distance D from
the system isocenter along one gradient axis. Preferably the
measurement is performed using the same receiver bandwidth to be
used during scanning. The pulse sequence used is illustrated in
FIG. 7 and includes a slice-select gradient waveform 604 applied
with an RF excitation pulse 602 to simply limit signal average
relative to hard pulse excitation. During this first acquisition,
no .DELTA.f(t) signal is applied (i.e., .DELTA.f(t)=0) and an NMR
free inductive decay (FID) signal is acquired as a series of
samples as indicated by acquisition window 608. The phase of the
acquired samples are calculated as described above. This pulse
sequence can be repeated a number of times (e.g., 20) and the data
averaged to increase the SNR of the measurement. The phase of the
measurements serve as the calibration data set .phi..sub.1(t).
[0049] The next step indicated at process block 610 in FIG. 6 is to
acquire a second set of calibration phase data .phi..sub.2(t). This
employs the same slice select waveform 604 and RF excitation pulse
602 as described above and shown in FIG. 7, but this time a
.DELTA.f(t) frequency modulation waveform 606 is applied to the
receiver as described above to offset the slice a distance D along
the gradient axis being calibrated. As shown in FIG. 6, the
.DELTA.f(t) frequency modulation waveform 606 is shaped like a
trapezoid having a plateau portion having an amplitude of
.DELTA.f.sub.P calculated according to Equation 1. The pulse
sequence is repeated and the phase of the samples acquired during
the window 608 are averaged to produce calibration data set
.phi..sub.2(t).
[0050] The next step as indicated by process block 614 is to
calculate the nominal phase, .phi..sub.NOMINAL, of the acquired NMR
signal samples .phi.2(t) as follows: .PHI. NOMINAL = 2 .times. .pi.
.times. .intg. 0 t .times. .DELTA. .times. .times. f .function. ( t
) .times. .times. d t ( 9 ) ##EQU3##
[0051] As indicated at process block 616, a phase error
E.sub..phi..DELTA.f(t) is now calculated from the phase values
.phi..sub.1(t), .phi..sub.2(t), and .phi..sub.NOMINAL. The phase
values .phi..sub.1(t) are measurements which include phase errors
E.sub..phi.B0 due to B0 field inhomogeneities:
.phi..sub.1(t)=E.sub..phi.B0(t) (10)
[0052] The phase values .phi..sub.2(t) are measurements which
include three phase components: the phase error E.sub..phi.B0 due
to B0 phase inhomogeneities; a phase error component
E.sub..phi..DELTA.f(t) caused by a timing delay between when the
frequency modulation waveform is applied to the down converter and
when the acquired RF signal is applied to the down converter in the
receiver; and the nominal phase .phi..sub.NOMINAL.
.phi..sub.2(t)=E.sub..phi..DELTA.B0(t)+E.sub..phi..DELTA.f(t)+.phi..sub.N-
OMINAL(t). (11)
[0053] Combining the last two equations, one can solve for phase
error E.sub..phi..DELTA.f(t):
E.sub..phi..DELTA.f(t)=.phi..sub.2(t)-[.phi..sub.NOMINAL(t)-.PHI..sub.1(t-
)]. (12)
[0054] This calculated phase error E.sub..phi..DELTA.f(t) will look
like waveform 609 in FIG. 7. As indicated at processing block 622,
using the calculated E.phi..DELTA.f(t), one can determine and
average values along the plateau at a plurality of points to
provide one value of phase error E.sub..phi.PLATEAU.
[0055] As indicated at process block 624, the phase error
E.sub..phi.PLATEAU is related to the timing error .tau..sub.D by
the following expression:
.tau..sub.D=E.sub..phi.PLATEAU/2.pi..DELTA.f.sub.P (13)
[0056] The timing error between the application of the .DELTA.f(t)
frequency modulation waveform and the received NMR signal may thus
be calculated with a high degree of accuracy.
[0057] The correction for the calculated timing errors E.sub.t or
.tau..sub.D can be made in two ways. First, a prospective
correction can be made during the image scan that follows the
prescan process described above. Prospective correction is
accomplished by shifting the timing of the frequency modulation
waveform .DELTA.f(t) by an amount E.sub.t or .tau..sub.D. Referring
to FIGS. 2 and 5, this delays the application of the waveform
.DELTA.f(t) to the receiver such that it precisely aligns with the
gradient waveform G(t) applied during the scan. As a result, the
phase error E.sub..theta.max or E.sub..phi.PLATEAU is not produced
during the subsequent acquisition of the image data during the
scan. While in theory this prospective correction can be made with
great precision, in practice this correction may have limited
precision because the waveforms that create .DELTA.f(t) are sampled
digitally and must begin and end at quantized intervals on the MRI
system.
[0058] Another prospective correction method may also be used. In
this case the correction is made by using a real-time phase
demodulation instead of or in addition to the frequency
demodulation. However, since the phase demodulation signal can
change amplitude at each time point, this can require significantly
more waveform memory than real-time frequency demodulation. As the
phase modulation waveform will often change for each repetition
time in a non-Cartesian pulse sequence, alternatively reloading the
waveform memory between repetition times is time-consuming and is
difficult to implement.
[0059] The timing error correction can also be made retrospectively
to the image data after it has been acquired. While this increases
the image reconstruction time, the retrospective correction is not
limited in accuracy by MRI system constraints that may prevent
accurate prospective correction.
[0060] The receiver demodulator assumes that the frequency
modulation waveform .DELTA.f(t) does not have any distortion, but
only a timing error during its operation. We can estimate the
experimentally applied phase information from the frequency
demodulation at each data acquisition time from the ideal gradient
waveform. .PHI. experimental .function. ( t ) = .times. 2 .times.
.pi. .times. .intg. - .infin. t .times. .DELTA. .times. .times. f
.function. ( t + .tau. ) .times. .times. d t = .times. 2 .times.
.pi. .times. .intg. - .infin. t .times. .gamma. .function. ( G x
.function. ( t + .tau. ) .times. d x + G y .function. ( t + .tau. )
.times. d y ) .times. .times. d t ( 14 ) ##EQU4## where
.phi..sub.experimental(t) is the experimentally applied phase from
the frequency demodulation, d.sub.x and d.sub.y are offset
distances in the x and y-axis in the units of cm, respectively.
[0061] The k-space position based on gradients x and y can be
expressed in Eq. (15) k x .function. ( t ) = .gamma. .times. .intg.
- .infin. t .times. G x .function. ( t ) .times. .times. d t
.times. .times. k y .function. ( t ) = .gamma. .times. .intg. -
.infin. t .times. G y .function. ( t ) .times. .times. d t ( 15 )
##EQU5## Hence
.phi..sub.experimental(t)=2.pi.[(k.sub.x(t+.tau.)d.sub.x+(k.sub.y(t+.tau.-
)d.sub.y] (16) where .phi..sub.experimental(t) represents the phase
that was demodulated in real time at the receiver. The actual phase
.phi..sub.desired(t) which should have been demodulated is given by
.PHI. desired .function. ( t ) = .times. 2 .times. .pi. .times.
.intg. - .infin. t .times. .DELTA. .times. .times. f .function. ( t
) = .times. 2 .times. .pi. .times. .intg. - .infin. t .times.
.gamma. .function. ( G xactual .function. ( t ) .times. d x + G
yactual .function. ( t ) .times. d y ) .times. .times. d t ( 17 )
##EQU6## .phi..sub.desired(t) is calculated based on the actual
gradient waveforms which are distorted from the ideal waveforms by
eddy currents and system timing delay, which may differ between
axes.
[0062] The actual gradient waveforms can be calculated by using a
known gradient calibration method. This calibration method provides
the correction of k-space trajectories based on actual gradient
waveforms G.sub.actual(t), and the actual k-space locations can be
expressed by Eq. (18). k xactual .function. ( t ) = .gamma. .times.
.intg. - .infin. t .times. G xactual .function. ( t ) .times.
.times. d t .times. .times. k yactual .function. ( t ) = .gamma.
.times. .intg. - .infin. t .times. G yactual .function. ( t )
.times. .times. d t ( 18 ) ##EQU7##
[0063] While the real-time frequency demodulation timing error is
the same on all axes, the errors due to gradient imperfections are
different, and hence are compensated for each axis. The k-space
positions thus obtained contain the effects of gradient errors and
represent the actual gradient waveforms that were applied from the
scanner.
[0064] Hence the phase which should have been modulated can be
rewritten as, .phi..sub.desired(t) =2.pi.[k.sub.x
actual(t)d.sub.x+k.sub.y actual(t)d.sub.y]. (19)
[0065] The difference .phi..sub.corr(t), between the desired and
the experimental phase
.phi..sub.corr(t)=.phi..sub.desired(t)-.phi..sub.experimental(t)
(20) is the amount of phase correction that has to be applied
retrospectively to each raw data point in the reconstruction. The
corrected raw data may also be gridded to the actual k-space
positions obtained from a k-space deviation calibration method.
Thus, both the phase and k-space location errors due to gradient
imperfections may be retrospectively compensated. Note that
.phi..sub.corr(t) increases as the image is acquired further away
from iso center. Phase correction is zero when imaging on iso
center. Hence there is no need of phase compensation due to timing
and gradient errors for on-axis or on-isocenter imaging.
* * * * *